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Integrating Formal Methods by Unifying Abstractions

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Integrated Formal Methods (IFM 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2999))

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Abstract

Integrating formal methods enhances their power as an intellectual tool in modelling and design. This holds regardless of automation, but a fortiori if software tools are conceived in an integrated framework.

Among the many approaches to integration, most valuable are those with the widest potential impact and least obsolescence or dependency on technology or particular tool-oriented paradigms. From a practical view, integration by unifying models leads to more uniform, wider-spectrum, yet simpler language design in automated tools for formal methods.

Hence this paper shows abstractions that cut across levels and boundaries between disciplines, help unifying the growing diversity of aspects now covered by separate formal methods and mathematical models, and even bridge the gap between “continuous” and “discrete” systems. The abstractions also yield conceptual simplification by hiding non-essential differences, avoiding repeating the same theory in different guises.

The underlying framework, not being the main topic, is outlined quite tersely, but enough for showing the preferred formalism to express and reason about the abstract paradigms of interest. Three such paradigms are presented in sufficient detail to appreciate the surprisingly wide scope of the obtained unification. The function extension paradigm is useful from signal processing to functional predicate calculus. The function tolerance paradigm spans the spectrum from analog filters to record types, relational databases and XML semantics. The coordinate space paradigm covers modelling issues ranging from transmission lines to formal semantics, stochatic processes and temporal calculi. One conclusion is that integrated formal methods are best served by calculational tools.

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References

  1. Aarts, C., Backhouse, R., Hoogendijk, P., Voermans, E., van der Woude, J.: A relational theory of data types. Report. Eindhoven University, Edinhoven (1992)

    Google Scholar 

  2. Abrial, J.-R.: B-Book. Cambridge University Press, Cambridge (1996)

    Book  MATH  Google Scholar 

  3. Alur, R., Sontag, E.D., Henzinger, T.A. (eds.): HS 1995. LNCS, vol. 1066. Springer, Heidelberg (1996)

    Google Scholar 

  4. Barendregt, H.P.: The Lambda Calculus—Its Syntax and Semantics, North- Holland (1984)

    Google Scholar 

  5. Bass, H.: The Carnegie Initiative on the Doctorate: the Case of Mathematics. Notices of the AMS 50(7), 767–776 (2003)

    Google Scholar 

  6. Bishop, R.H.: Learning with LabVIEW. Addison-Wesley Longman, Amsterdam (1999)

    Google Scholar 

  7. Blahut, R.E.: Theory and Practice of Error Control Codes. Addison-Wesley, Reading (1984)

    Google Scholar 

  8. Boute, R.T.: On the requirements for dynamic software modification. In: van Spronsen, C.J., Richter, L. (eds.) MICROSYSTEMS: Architecture, Integratio and Use (Euromicro Symposium 1982), North Holland, pp. 259–271 (1982)

    Google Scholar 

  9. Boute, R.T.: A calculus for reasoning about temporal phenomena. In: Proc. NGI-SION Symposium 4, pp. 405–411 (April 1986)

    Google Scholar 

  10. Boute, R.T.: System semantics and formal circuit description. IEEE Transactions on Circuits and Systems CAS-33(12), 1219–1231 (1986)

    Article  Google Scholar 

  11. Boute, R.T.: Systems Semantics: Principles, Applications and Implementation. ACM TOPLAS 10(1), 118–155 (1988)

    Article  Google Scholar 

  12. Boute, R.T.: Fundamentals of Hardware Description Languages and Declarative Languages. In: Mermet, J.P. (ed.) Fundamentals and Standards in Hardware Description Languages, pp. 3–38. Kluwer, Dordrecht (1993)

    Google Scholar 

  13. Boute, R.T.: Funmath illustrated: A Declarative Formalism and Application Examples. Computing Science Institute, University of Nijmegen (July 1993)

    Google Scholar 

  14. Boute, R.T.: Supertotal Function Definition in Mathematics and Software Engineering. IEEE Transactions on Software Engineering 26(7), 662–672 (2000)

    Article  Google Scholar 

  15. Boute, R.T.: Functional Mathematics: a Unifying Declarative and Calculational Approach to Systems, Circuits and Programs — Part I: Basic Mathematics. Course text, Ghent University (2002)

    Google Scholar 

  16. Boute, R.T.: Concrete Generic Functionals: Principles, Design and Applications. In: Gibbons, J., Jeuring, J. (eds.) Generic Programming, pp. 89–119. Kluwer, Dordrecht (2003)

    Google Scholar 

  17. Boute, R., Verlinde, H.: Functionals for the Semantic Specification of Temporal Formulas for Model Checking. In: König, H., Heiner, M., Wolisz, A. (eds.) FORTE 2003 Work-in-Progress Papers. BTU Cottbus Computer Science Reports, pp. 23–28 (2003)

    Google Scholar 

  18. Bracewell, R.N.: The Fourier Transform and Its Applications, 2nd edn. McGraw-Hill, New York (1978)

    MATH  Google Scholar 

  19. Carson, R.S.: Radio Communications Concepts: Analog. Wiley, Chichester (1990)

    Google Scholar 

  20. Clarke, E.M., Gromberg, O., Peled, D.: Model Checking. MIT Press, Cambridge (2000)

    Google Scholar 

  21. Dijkstra, E.W., Scholten, C.S.: Predicate Calculus and Program Semantics. Springer, Heidelberg (1990)

    MATH  Google Scholar 

  22. Dwyer, M.B., Hatcliff, J.: Bandera Temporal Specification Patterns. In: Tutorial presentation at ETAPS 2002 (Grenoble) and SFM 2002, Bertinoro (2002), http://www.cis.ksu.edu/santos/bandera/Talks/SFM02/02-SFM-Patterns.ppt

  23. Franklin, G.F., David Powell, J., Emami-Naeini, A.: Feedback Control of Dynamic Systems. Addison-Wesley, Reading (1986)

    MATH  Google Scholar 

  24. Gries, D.: Improving the curriculum through the teaching of calculation and discrimination. Communications of the ACM 34 3, 45–55 (1991)

    Google Scholar 

  25. Gries, D., Schneider, F.B.: A Logical Approach to Discrete Math. Springer, Heidelberg (1993)

    MATH  Google Scholar 

  26. Gries, D.: The need for education in useful formal logic. IEEE Computer 29 4, 29–30 (1996)

    Google Scholar 

  27. Gries, D.: Foundations for Calculational Logic. In: Broy, M., Schieder, B. (eds.) Mathematical Methods in Program Development. NATO ASI Series F, vol. 158, pp. 83–126. Springer, Heidelberg (1997)

    Google Scholar 

  28. Grossman, R.L., Nerode, A., Ravn, A.P., Rischel, H. (eds.): HS 1991 and HS 1992. LNCS, vol. 736. Springer, Heidelberg (1993)

    Google Scholar 

  29. Hanna, K., Daeche, N., Howells, G.: Implementation of the Veritas design logic. In: Stavridou, V., Melham, T.F., Boute, R.T. (eds.) Theorem Provers in Circuit Design, North Holland, pp. 77–84 (1992)

    Google Scholar 

  30. Hehner, E.C.R.: From Boolean Algebra to Unified Algebra. Internal Report, University of Toronto (June 1997) (revised 2003)

    Google Scholar 

  31. Hoare, C.A.R., Jifeng, H.: Unifying Theories of Programming. Prentice-Hall, Englewood Cliffs (1998)

    Google Scholar 

  32. Holzmann, G.: The SPIN Model Checker: Primer and Reference Manual. Addison-Wesley, Reading (2003)

    Google Scholar 

  33. Hudak, P., Peterson, J., Fasel, J.H.: A Gentle Introduction to Haskell 98 (October 1999), http://www.haskell.org/tutorial/

  34. Jensen, K., Wirth, N.: PASCAL User Manual and Report. Springer, Heidelberg (1978)

    Google Scholar 

  35. Lamport, L.: Specifying Systems. Addison-Wesley, Reading (2002)

    Google Scholar 

  36. Lee, E.A., Messerschmitt, D.G.: Digital Communication, 2nd edn. Kluwer, Dordrecht (1994)

    Google Scholar 

  37. Manna, Z., Pnueli, A.: The Temporal Logic of Reactive and Concurrent Systems — Specification. Springer, Heidelberg (1992)

    Google Scholar 

  38. Manolios, P., Strother Moore, J.: On the desirability of mechanizing calculational proofs. Information Processing Letters 77(2-4), 173–179 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  39. Meyer, B.: Introduction to the Theory of Programming Languages. Prentice-Hall, Englewood Cliffs (1991)

    Google Scholar 

  40. Owre, S., Rushby, J., Shankar, N.: PVS: prototype verification system. In: Kapur, D. (ed.) CADE 1992. LNCS, vol. 607, pp. 748–752. Springer, Heidelberg (1992)

    Google Scholar 

  41. Papoulis, A.: Probability, Random Variables and Atochastic Processes. McGraw-Hill, New York (1965)

    Google Scholar 

  42. Paulson, L.C.: Introduction to Isabelle. Computer Laboratory University of Cambridge (Febraury 2001), http://www.cl.cam.ac.uk/Research/HVG/Isabelle/dist/docs.html

  43. Parzen, E.: Modern Probability Theory and Its Applications. Wiley, Chichester (1960)

    MATH  Google Scholar 

  44. Vaandrager, F.W., van Schuppen, J.H. (eds.): HSCC 1999. LNCS, vol. 1569. Springer, Heidelberg (1999)

    MATH  Google Scholar 

  45. Vardi, M.Y., Wolper, P.: An automata-theoretic approach to automatic program verification. In: Proc. Symp. on Logic in Computer Science, June 1986, pp. 322–331 (1986)

    Google Scholar 

  46. Verlinde, H.: Systematisch ontwerp van XML-hulpmiddelen in een functionele taal. M.Sc. Thesis, Ghent University (2003)

    Google Scholar 

  47. Wigner, E.: The Unreasonable Effectiveness of Mathematics in the Natural Sciences. Comm. Pure and Appl. Math. 13(I), 1–14 (1960), http://nedwww.ipac.caltech.edu/level5/March02/Wigner/Wigner.html

    Article  MATH  Google Scholar 

  48. Winskel, G.: The Formal Semantics of Programming Languages: An Introduction. MIT Press, Cambridge (1993)

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. INTEC, Ghent University, Belgium

    Raymond Boute

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  1. Raymond Boute
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Editor information

Editors and Affiliations

  1. Computing Laboratory, University of Kent, CT2 7NF, Canterbury, Kent, UK

    Eerke A. Boiten

  2. Department of Computing, University of Sheffield, S1 4DP, Sheffield, UK

    John Derrick

  3. School of Information Technology and Electrical Engineering, The University of Queensland, 4072, Australia

    Graeme Smith

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Boute, R. (2004). Integrating Formal Methods by Unifying Abstractions. In: Boiten, E.A., Derrick, J., Smith, G. (eds) Integrated Formal Methods. IFM 2004. Lecture Notes in Computer Science, vol 2999. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24756-2_24

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  • DOI: https://doi.org/10.1007/978-3-540-24756-2_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-21377-2

  • Online ISBN: 978-3-540-24756-2

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